Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y + 6)(y - 8)
(y x y) + (y x -8) + (6 x y) + (6 x -8)
y² - 8y + 6y - 48
y² - 2y - 48

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the > sign and the answer on the other.

2b - 5 > -7 + b
2b > -7 + b + 5
2b - b > -7 + 5
b > -2

A trapezoid is a quadrilateral with one set of parallel sides.

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

b² - 2b - 5 = -4b - 2
b² - 2b - 5 + 2 = -4b
b² - 2b + 4b - 3 = 0
b² + 2b - 3 = 0

Next, factor the quadratic equation:

b² + 2b - 3 = 0
(b - 1)(b + 3) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 1) or (b + 3) must equal zero:

If (b - 1) = 0, b must equal 1
If (b + 3) = 0, b must equal -3

So the solution is that b = 1 or -3